Rail to rail OTA with folded cascode stage (transistors sizes)

Hi everyone,
I'm trying to design a rail-to-rail amplifier with a folded-cascode stage (differential to single-ended stage). I have a 20µA bias. However, I have not succeeded in having a large bandwidth (it should be 40MHz) and I don't know how to do to obtain it. I can't increase current and sizes too much.
Do you know how can I do to have a correct bandwidth ?
And also, how are cascode transistors sizes usually chosen ?
I have designed smaller structures but for this one, I am a bit confused on the method.
Thanks

Hey there, gm/C is your ultimate limitation. So you need to specify the load of this circuit too before speculating its bandwidth.

But in general, there isn't a simple way to increase the bandwidth without having to increase the current for the same load capacitance. And 40 MHz is actually a large bandwidth. As a rule of thumb you can say, small devices with large currents yield a higher bandwidth. But there are of course exceptions. So this is basically how you obtain the bandwidth.

Cascode transistor sizes are usually chosen as the same as the original current source for simplicity and easier layout, but you can write a book about them. For example if you have current sources with long L's, you might want to keep your cascodes with shorter L's to make sure their parasitics don't affect the overall response. If it comes to very high gain, sometimes you have to do source bulk connection and bias and size accordingly. So there's a lot in that subject.

Thanks for your answer, it makes thing clearer. I have defined the capacitive load (10pF).

However, because of the PMOS current mirror that biases the PMOS input pair, I can't increase current a lot because transistors rapidly goes towards linear region.

Anyway, I was asked to use this structure as a voltage follower with quite unclear specifications. It works fine. But do I really need a high open-loop gain for a voltage follower ? And I'm quite confused on the bandwidth definition that matters. If I need my voltage follower to work up to 40Mhz, what should I consider ? Open loop bandwidth @-3dB, open loop unity gain bandwidth or the same in closed loop ?
In fact I understand the specifications needed/ given for an operational amplifier. But for the voltage follower, I'm not sure what really matters in term of gain and bandwidth and what structure is the most adapted to design it.

And when I use a rail-to-rail voltage follower, is it important to add a structure to keep gm constant on the common mode input range ?

First, I would suggest following a book on opamp design. Because most of the questions you asked are already answered questions.

Nevertheless, I can give directions for a starting point.

1- You can increase the current without increasing vdssat for current sources. It just ends up a huge device which is not very desirable at source node because that node defines your high frequency distortion. You should already reap the most gm out of your input devices anyway, so I don't know what else I can add.

2- Accuracy of a negative feedback loop depends on the loop gain. Ideally if the loop gain is high, the error goes to zero. This is an error that you'd see as offset when the opamp is used as a voltage buffer. This offset also changes with the voltage level, so it causes errors too. So for better THD increasing gain is also essential, which conflicts the speed requirement when high frequency is concerned.

3- Unity gain bandwidth is the bandwidth you'd get after configuring it as voltage follower. Or UGB/2 is your bandwidth when you have a gain of two amplifier. Or 2*UGB if you have a 1/2 amplifier, but this messes up stability most of the time.
You can measure the ac performances of different configurations to verify these. Don't even design an opam use vcvs + RC network. Actually this is what you should've done before starting the design, and get the specifications for the opamp with this model.

4- Again in high accuracy applications yes you need to. In most switched cap applications you can get away with switching the tail current. But in cont. time applications that may not be enough. So as always it depends.